SUMMARYThe paper presents a strainhardening constitutive model for unsaturated soil behaviour based on energy conjugated stress variables in the framework of superposed continua. The proposed constitutive law deals with hydro-mechanical coupling phenomena. The main purpose is to develop within a consistent framework a model that can deal with possible mechanical instabilities occurring in partially saturated materials. The loss of capillary effects during wetting processes can, in fact, play a central role in unstable processes. Therefore, it will be shown that the bonding effects due to surface tensions can be described in a mathematical framework similar to that employed for bonded geomaterials to model weathering or diagenesis effects, either mechanically or chemically induced. The results of several simulations of common laboratory tests on partially saturated soil specimens are shown. The calculated behaviour appears to be in good qualitative agreement with that observed in the laboratory. In particular it is shown that volumetric collapse phenomena due to hydraulic debonding effects can be successfully described by the model. Finally, it will be highlighted the ability of the model to naturally capture the transition to a fully saturated condition and to deal with possible mechanical instabilities in the unsaturated regime.

The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting-induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro-mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second-order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro-mechanical instabilities are then interpreted in the light of this second-order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro-mechanical instabilities can be predicted using an extended form of Hill's stability criterion

a b s t r a c tIn this paper the onset of instabilities in elastoplastic materials is theoretically studied and a conceptual basis for understanding the physical implications of a loss of uniqueness and/or existence of the incremental response is provided. For this purpose, the concept of test controllability is reinterpreted and mixed stress-strain loading programmes are accounted for. A set of scalar indices, the moduli of instability, related with the inception of an unstable response is introduced and their dependency on the loading programme is explicitly illustrated. The paper shows that the use of these newly defined scalar measures provides support for an alternative definition for mechanical stability, which is closely related with the mathematical notions of existence and uniqueness of the predicted incremental response. In the final section, some mathematical properties of the moduli of instability are discussed, suggesting a novel reinterpretation of other well established theories and providing additional tools for the future application of the proposed framework.

A complete thermodynamic theory is presented that is capable of explaining the dependence of yielding on the degree of saturation in brittle granular aggregates. Historically, constitutive models represented this coupling between mechanics and hydraulics only phenomenologically, by way of the incorporation of the loading collapse curve concept. This was done both for fine-grained and granular soils, and, for the latter case, without embodying the physical connection of yielding to elasticity, as motivated by fracture mechanics. Here, this connection is captured by the breakage mechanics theory, which underpins a grain-size scaling of the mechanical part of the Helmholtz free energy potential. In addition, an explicit reliance of this potential on hydraulic measures is explored, with another grain-size scaling inspired by the capillary theory. It is shown that through homogenisation these two scaling laws motivate a total macroscopic Helmholtz free energy that, together with the breakage dissipation, captures the salient couplings between mechanics and hydraulics properties, while showing a promising agreement with experiments.

SUMMARYThe paper presents a theoretical approach to deal with mechanical instabilities in unsaturated soils. Towards this goal, the concept of test controllability is extended to a hydro-mechanically coupled framework. A constitutive approach based on the introduction of hydraulic generalized stress-strain variables is first adopted, in order to better describe suction effects on the mechanical behaviour of soil. The mathematical consequences of hydro-mechanical coupling are presented next and two indices are defined to identify the onset of an instability. Possible instability modes linked to saturation processes are discussed. It is shown that the way in which the hydraulic variables are controlled in tests on unsaturated soil specimens is the key factor for the possible occurrence of instabilities and the consequent loss of test controllability. It is shown in particular that unsaturated soil specimens are prone to instability when an externally controlled water flux is injected into the specimen (inundation). This result could in part explain the sudden collapse of soil specimens subjected to wetting under constant applied stresses, which is observed both in the laboratory and in the field.